Multiscale Geographically Weighted Regression (MGWR)

Standard GWR calibrates one bandwidth shared by all predictors, implying that every relationship varies at the same geographic scale. MGWR estimates a separate, optimised bandwidth for each predictor, so some relationships can be nearly global (large bandwidth, smooth surface) while others are highly local (narrow bandwidth, rapidly varying surface).

A large bandwidth means the model needs to borrow information from many distant observations to estimate that predictor's coefficient, which indicates the relationship is spatially stationary or near-global. In the limit, an infinitely large bandwidth produces the same coefficient estimate as OLS for that predictor.

Use the Monte Carlo significance test implemented in the mgwr library: it repeatedly randomises the residuals and checks whether the observed variability in a coefficient surface exceeds what random permutations would produce. This is more reliable than simply inspecting whether local t-statistics exceed 1.96.

Standard MGWR is designed for cross-sectional data. Temporal extensions (e.g., GTWR or panel spatial models) exist but are separate frameworks. If your data have repeated observations over time, consider a spatial panel model or Geographically and Temporally Weighted Regression instead.

There is no strict rule, but local regression becomes unreliable when too few observations are available near each location. In practice, samples below 100 observations often lead to unstable local estimates, especially with narrow bandwidths. Larger samples (200+) with reasonable spatial coverage are preferred.